one can define an effective Hamiltonian as the expectation value \(H_{\rm eff}=\langle \hat{H}\rangle \)  of the corresponding Hamilton operator, taken in
an arbitrary state. The effective Hamiltonian is therefore a function on the
state space of the system. A systematic semiclassical description
parameterizes suitable states by their expectation values of basic operators,
\(q=\langle \hat{q}\rangle \)  and \(p=\langle \hat{p}\rangle \) , as well as a series
of moments such as
\(\Delta (q^n)=\langle (\hat{q}-\langle \hat{q}\rangle )^n\rangle \) . Taking into
account ordering choices, we follow [1]}, [2]} and define a specific
set of moments of a state by
\( \Delta (q^np^m)=\langle (\hat{q}-\langle \hat{q}\rangle )^n(\hat{p}-\langle \hat{p}\rangle )^m\rangle _{\rm symm}\) 
